>"In the axiomatic schemata of the Scott–Lemmon form, the number of consecutively stacked modal operators determines the composition of the accessibility relation in the corresponding frame condition. Each block corresponds to then-fold composition Rthereby determining the accessibility paths that appear in the frame condition."
This doesn't mean anything to me and I don't think anything of it
>>16929770Modal logic and therefore every other branch of math, and therefore most science is a game invented by people for the people.Entropy has made it such that our intelligence has stagnated and we can't grasp the intricacies and delicacies of The Universe therefore we develop offshoots of math etc. et al to disilussion ourselves that we are in control, that we are smart.
>>16929822Well maybe you should start thinking something of it.
I find it appealing for three reasons.* I'm not a fan of the weakening principle [math] A\to (B\to A) [/math], and strong implication of modal logic doesn't validate it. (I can expand on this point)* Intuitionistic logic embeds into S4 logic, and that reading of it is I think somewhat closer to the epistemological reading of intuitionistic logic* Mathematicians (unlike say CS people) have always been extremely uncreative with their logical foundations, since set theory, and I'd like to see math on different logics. Since set theory can model everything, this is sorta justified - you can code/mimic anything in set theory over classical logic. But it means everything is extremely not native and I think we leave some ideas on the table.
>>16929897>* Intuitionistic logic embeds into S4 logic, and that reading of it is I think somewhat closer to the epistemological reading of intuitionistic logicCould you please expand on this point? How is it embedded?
So basically its like a quantum computer, the initial setup conditions determine which outcomes you can possibly receive
>>16929941The axioms you assume will affect what kind of frame conditions you have that in turn will make any of your theorems semantically valid.